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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 932019, 17 pages
http://dx.doi.org/10.1155/2012/932019
Research Article

Solvability of Nonlinear Integral Equations of Volterra Type

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 2 August 2012; Accepted 23 October 2012

Academic Editor: Kishin B. Sadarangani

Copyright © 2012 Zeqing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. P. Agarwal, D. O'Regan, and P. J. Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999. View at Zentralblatt MATH
  2. T. A. Burton, Volterra Integral and Differential Equations, vol. 167, Academic Press, Orlando, Fla, USA, 1983. View at Zentralblatt MATH
  3. D. O'Regan and M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, vol. 445, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. R. Arias, R. Benítez, and V. J. Bolós, “Nonconvolution nonlinear integral Volterra equations with monotone operators,” Computers and Mathematics with Applications, vol. 50, no. 8-9, pp. 1405–1414, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. Banaś and A. Chlebowicz, “On existence of integrable solutions of a functional integral equation under Carathéodory conditions,” Nonlinear Analysis, vol. 70, no. 9, pp. 3172–3179, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. Banaś and B. C. Dhage, “Global asymptotic stability of solutions of a functional integral equation,” Nonlinear Analysis, vol. 69, no. 7, pp. 1945–1952, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. Banaś and K. Goebel, “Measures of noncompactness in banach spaces,” in Lecture Notes in Pure and Applied Mathematics, vol. 60, Marcel Dekker, New York, NY, USA, 1980.
  8. J. Banaś, J. Rocha, and K. B. Sadarangani, “Solvability of a nonlinear integral equation of Volterra type,” Journal of Computational and Applied Mathematics, vol. 157, no. 1, pp. 31–48, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J. Banaś and B. Rzepka, “On existence and asymptotic stability of solutions of a nonlinear integral equation,” Journal of Mathematical Analysis and Applications, vol. 284, no. 1, pp. 165–173, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. J. Banaś and B. Rzepka, “An application of a measure of noncompactness in the study of asymptotic stability,” Applied Mathematics Letters, vol. 16, no. 1, pp. 1–6, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J. Banaś and B. Rzepka, “On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation,” Applied Mathematics and Computation, vol. 213, no. 1, pp. 102–111, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. T. A. Burton and B. Zhang, “Fixed points and stability of an integral equation: nonuniqueness,” Applied Mathematics Letters, vol. 17, no. 7, pp. 839–846, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. A. Constantin, “Monotone iterative technique for a nonlinear integral equation,” Journal of Mathematical Analysis and Applications, vol. 205, no. 1, pp. 280–283, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. B. C. Dhage, “Local asymptotic attractivity for nonlinear quadratic functional integral equations,” Nonlinear Analysis, vol. 70, no. 5, pp. 1912–1922, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. W. G. El-Sayed, “Solvability of a neutral differential equation with deviated argument,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 342–350, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. X. L. Hu and J. R. Yan, “The global attractivity and asymptotic stability of solution of a nonlinear integral equation,” Journal of Mathematical Analysis and Applications, vol. 321, no. 1, pp. 147–156, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. S. Jung, “Asymptotic behavior of solutions of nonlinear Volterra equations and mean points,” Journal of Mathematical Analysis and Applications, vol. 260, no. 1, pp. 147–158, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. Z. Liu and S. M. Kang, “Existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type,” The Rocky Mountain Journal of Mathematics, vol. 37, no. 6, pp. 1971–1980, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. Z. Liu and S. M. Kang, “Existence and asymptotic stability of solutions to a functional-integral equation,” Taiwanese Journal of Mathematics, vol. 11, no. 1, pp. 187–196, 2007. View at Zentralblatt MATH
  20. D. O'Regan, “Existence results for nonlinear integral equations,” Journal of Mathematical Analysis and Applications, vol. 192, no. 3, pp. 705–726, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. C. A. Roberts, “Analysis of explosion for nonlinear Volterra equations,” Journal of Computational and Applied Mathematics, vol. 97, no. 1-2, pp. 153–166, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. M. A. Taoudi, “Integrable solutions of a nonlinear functional integral equation on an unbounded interval,” Nonlinear Analysis, vol. 71, no. 9, pp. 4131–4136, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. G. Darbo, “Punti uniti in trasformazioni a codominio non compatto,” Rendiconti del Seminario Matematico della Università di Padova, vol. 24, pp. 84–92, 1955. View at Zentralblatt MATH